The well-known connection between hyperidentities of an algebra and identities satisfied by the clone of this algebra is studied here in a restricted setting, that of n-ary strongly full hyperidentities and identities of the n-ary clone of term operations of an algebra induced by strongly full terms, both of a type consisting only of n-ary operation symbols. We call such a type an n-ary type. U...

A q-ary maximum distance separable (MDS) code C with length n, dimension k over an alphabet A of size q is a set of qk codewords that are elements of An, such that the Hamming distance between two distinct codewords in C is at least n− k+1. Sets of mutually orthogonal Latin squares of orders q ≤ 9, corresponding to two-dimensional q-ary MDS codes, and q-ary one-error-correcting MDS codes for q ...

Discovering new integer sequences and generalizing the existing ones are important and of great interest. In this article, various balanced k-ary trees are first studied and their taxonomy is built. In particular, two systematic balanced k-ary trees, whose nth tree is determined by a certain algorithm, are identified, i.e., complete and sizebalanced k-ary trees. The integer sequences from the f...